Equations of motion in a generalized theory of gravitation

1981 ◽  
Vol 59 (11) ◽  
pp. 1723-1729 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
Static Solution ◽  
Coupling Constant ◽  
Field Equations ◽  
Complete Space ◽  
Test Particles ◽  
Theory Of Gravitation ◽  
Definition Of ◽  
Universal Coupling

The problem of the motion of test particles is studied in a theory of gravitation based on a nonsymmetric gμν. According to the conservation laws the test particles can follow two kinds of geodesies, depending on the definition of a local inertial frame in the theory. One of these geodesies is nonmaximal and leads to a timelike and null world line complete space when a new parameter l, that occurs as a constant of integration in the spherically symmetric, static solution of the field equations, satisfies [Formula: see text]. In the theory, the parameter [Formula: see text] where N is the number of fermions in a system and a is a new universal coupling constant that satisfies [Formula: see text]. The physical implications of l and the associated conservation law of fermion number is discussed in detail.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

The equations of motion in the non-symmetric unified field theory

1954 ◽  
Vol 226 (1166) ◽  
pp. 366-377 ◽  
Keyword(s):  
Equations Of Motion ◽  
Coulomb Force ◽  
Unified Field Theory ◽  
Field Equations ◽  
Original Theory ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
The One ◽  
A Charge ◽  
Weak Fields

The field equations of the non-symmetric unified theory of gravitation and electromagnetism are changed so that they imply the existence of the Coulomb force between electric charges. It is shown that the equations of motion of charged masses then follow correctly to the order of approximation considered. The equations for weak fields in the modified theory are derived and shown to lead to Maxwell’s equations together with a restriction on the current density. This restriction is different from that in the original theory, and in the static, spherically symmetric case permits a charge distribution more likely to correspond to a particle. The failure of the original theory to lead to the equations of motion is related to the structure of the quantities appearing in it, and reasons are given for supposing that no nonsymmetric theory simpler than the one put forward is likely to give these equations in their conventional form.

scholarly journals Effective Perihelion Advance and Potentials in a Conformastatic Background with Magnetic Field

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Abraão J. S. Capistrano ◽  
Antonio C. Gutiérrez-Piñeres
Keyword(s):  
Magnetic Field ◽  
Equations Of Motion ◽  
The Moon ◽  
Field Equations ◽  
Effective Potentials ◽  
Test Particles ◽  
Perihelion Advance ◽  
Theoretical Predictions ◽  
Analytic Expression ◽  
The Magnetic Field

Exact solutions of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources are investigated. In this context, effective potentials are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of the equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the solar system and the Moon (EPM2011). In general, we show that the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein’s gravity alone.

The Annotated Manuscript

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Equations Of Motion ◽  
Special Theory ◽  
Material Point ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Theory Of Gravitation

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory of relativity, taking into account Einstein's fundamental considerations on the postulate of relativity, and more specifically why he went beyond the special theory of relativity. It then considers the spacetime continuum, explaining the role of coordinates in the new theory of gravitation. It also describes tensors of the second and higher ranks, multiplication of tensors, the equation of the geodetic line, the formation of tensors by differentiation, equations of motion of a material point in the gravitational field, the general form of the field equations of gravitation, and the laws of conservation in the general case. Finally, the behavior of rods and clocks in the static gravitational field is examined.

scholarly journals MASSLESS SPINNING TEST PARTICLES IN ALGEBRAICALLY SPECIAL VACUUM SPACE–TIMES

2006 ◽  
Vol 15 (05) ◽  
pp. 737-758 ◽  
Author(s):  
DONATO BINI ◽  
CHRISTIAN CHERUBINI ◽  
ANDREA GERALICO ◽  
ROBERT T. JANTZEN
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
Space Time ◽  
Null Direction ◽  
Massless Particles ◽  
Special Vacuum ◽  
Test Particles ◽  
Vacuum Space

The motion of massless spinning test particles is investigated using the Newman–Penrose formalism within the Mathisson–Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole reduction world line" lies along a principal null direction of an algebraically special vacuum space–time, the equations of motion can be explicitly integrated. Examples are given for some familiar space–times of this type in the interest of shedding some light on the consequences of this model.

scholarly journals PALATINI FORMULATION OF MODIFIED GRAVITY WITH A NON-MINIMAL CURVATURE-MATTER COUPLING

2011 ◽  
Vol 26 (20) ◽  
pp. 1467-1480 ◽  
Author(s):  
TIBERIU HARKO ◽  
TOMI S. KOIVISTO ◽  
FRANCISCO S. N. LOBO
Keyword(s):  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Scalar Fields ◽  
Momentum Tensor ◽  
Nonlinear Dependence ◽  
Modified Theories Of Gravity ◽  
Field Equations ◽  
Test Particles ◽  
Theories Of Gravity ◽  
Minimal Curvature

We derive the field equations and the equations of motion for scalar fields and massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi–Cività connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the nonconservation of the energy–momentum tensor. We derive the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity. It is pointed out here that the force is of a different nature than in the metric formalism. We also consider the implications of a nonlinear dependence of the action upon the matter Lagrangian.

scholarly journals Wave-like spatially homogeneous models of Stackel spacetimes (3.1) type in the scalar-tensor theory of gravity

2020 ◽  
Vol 17 (12) ◽  
pp. 2050184
Author(s):  
Evgeny Osetrin ◽  
Konstantin Osetrin ◽  
Altair Filippov ◽  
Ilya Kirnos
Keyword(s):  
Eikonal Equation ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Scalar Tensor Theory ◽  
Tensor Theory ◽  
Test Particles ◽  
Petrov Classification ◽  
Homogeneous Models ◽  
Theory Of Gravitation ◽  
Spatially Homogeneous

All classes of spatially homogeneous spacetime models in the generalized scalar–tensor theory of gravitation are found to allow the integration of the equations of motion of test particles and the eikonal equation by the method of separation of variables by type (3.1). Three classes of exact solutions are obtained that relate to Shapovalov wave-like spacetime models. The resulting spacetime models are of types IV, VI and VII according to the Bianchi classification and type N according to Petrov classification.

scholarly journals I. Identifications

1938 ◽  
Vol 165 (922) ◽  
pp. 313-332 ◽  
Keyword(s):  
Classical Theory ◽  
Equations Of Motion ◽  
Laws Of Nature ◽  
Mechanical Force ◽  
Magnetic Intensity ◽  
Field Equations ◽  
Physical Assumption ◽  
General Object ◽  
Definition Of ◽  
Magnetic Poles

1. The general object of the following papers is to ascertain what form the equations of electromagnetism take when derived on a purely kinematic basis. Maxwell’s theory is not assumed. The only physical assumption made, namely, that a system of moving charges conserves its energy (defined kinematically) when the accelerations of the charges vanish, is a very slight one and is certainly satisfied in classical electromagnetism, but the resulting equations and laws, whilst coinciding with the classical theory to a considerable extent, differ in certain essential particulars. This arises from the avoidance of the empirical laws and hypothetical assumptions from which Maxwell’s theory starts. In particular we avoid the formal inconsistency in the classical theory by which a magnetic intensity H is defined via the mechanical force on an isolated magnetic pole, yet isolated magnetic poles do not occur in the classical “theory of electrons”. In the present treatment a magnetic intensity is defined via the mechanical force on a moving “charged” particle, as an element entering into the calculation of such force. The general method is, adopting the dynamics constructed in previous papers on a purely kinematic basis (Milne 1936, 1937), to formulate equations of motion containing the next most general type of “external” force arising after “gravitational” forces have been dealt with. Such forces arise from the double differentiation of scalar “superpotentials”, but we do not lay down what form these scalars are to take. Instead we allow them to determine themselves, by imposing the single physical assumption above-mentioned, after the equation of energy has been derived. Once the scalar superpotentials have been so determined, their double differentiation yields symbols E, H, which are then compared with the empirical laws governing the interaction of “charges”; this allows us to identify the adopted definition of charge and the symbols E, H with the similar quantities occurring in the experimental formulation. Lastly, we derive the identities satisfied by the resulting E, H; these partly coincide with, and partly differ from, the “field equations” with which the classical theory starts, and thus we end with theorems which play the part of the “laws of nature” assumed at the outset in the classical theory.

Bending-Bending Mode of a Rotating Tapered-Twisted Turbomachine Blade Including Rotatory Inertia and Shear Deformation

1969 ◽  
Vol 91 (4) ◽  
pp. 1017-1024 ◽  
Author(s):  
R. M. Krupka ◽  
A. M. Baumanis
Keyword(s):  
Shear Deformation ◽  
Equations Of Motion ◽  
Torsional Vibrations ◽  
Parameter System ◽  
Field Equations ◽  
Lagrange Equations ◽  
Rotatory Inertia ◽  
Lumped Parameter ◽  
Bending Mode ◽  
Definition Of

This paper presents the effect on natural frequency and mode shape of the inclusion of terms that are present in the general equations of motion to describe phenomena associated with Rotatory Inertia and Shear Deformation. The coupling that exists between the flexural and torsional vibrations is not considered. Carnegie’s formulation of the Lagrange Equations of motion is used and the set of field equations solved using Myklestad’s adaptation of the Holzer method. The definition of the lumped parameter system used and the derivation of the associated discrete “difference equations,” which are utilized in the computer approach to the boundary value problem considered, constitute an extension of the Carnegie work.

Long range forces and broken symmetries

1973 ◽  
Vol 333 (1595) ◽  
pp. 403-418 ◽  
Keyword(s):  
Gravitational Constant ◽  
Equations Of Motion ◽  
Vacuum Field ◽  
Field Equations ◽  
Field Function ◽  
Closed Loops ◽  
Broken Symmetries ◽  
Action Integral ◽  
Theory Of Gravitation ◽  
Set Up

There are reasons for believing that the gravitational constant varies with time. Such a variation would force one to modify Einstein’s theory of gravitation. It is proposed that the modification should consist in the revival of Weyl’s geometry, in which lengths are non-integrable when carried around closed loops, the lack of integrability being connected with the electromagnetic field. A new action principle is set up, much simpler than Weyl’s, but requiring a scalar field function to describe the gravitational field, in addition to the g μν . The vacuum field equations are worked out and also the equations of motion for a particle. An important feature of Weyl’s geometry is that it leads to a breaking of the C and T symmetries, with no breaking of P or of CT . The breaking does not show itself up with the simpler kinds of charged particles, but requires a more complicated kind of term in the action integral for the particle.

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